ARLINGTON, Texas — Trey Burke shook off one of his worst starts with the best shot of his life.

Burke bounced back from a scoreless first half to score 23 points, including a long, never-a-doubt 3-pointer in the final seconds of regulation, and Michigan rallied to beat Kansas, 87-85, in overtime in the South Regional semifinals Friday night.

The fourth-seeded Wolverines wiped out a 10-point Kansas lead in the last three minutes of regulation, and Burke gave them their first lead since early in the game with another long three to open Michigan’s scoring in overtime.

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‘‘This guy was a champ all the way through it,’’ Michigan coach John Beilein said.

The Wolverines (29-7) reached the regional finals for the first time since the Fab Five era 19 years ago, the last time they were in the round of 16.

Ben McLemore had 20 points to lead the Jayhawks (31-6), who looked to be on their way to a third straight regional final before Michigan’s improbable rally. Instead, they became the third No. 1 seed to fall in this tournament, joining Gonzaga and Indiana.

The Wolverines were down 5 when Tim Hardaway Jr. missed a 3-pointer with 35 seconds left, but Glenn Robinson III won a scramble for the ball and hit a reverse layup to force Kansas to win the game at the free throw line.

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The Jayhawks couldn’t do it. Burke’s tying shot — he pulled up from well beyond the arc just right of key — came with 4.2 seconds left after Elijah Johnson missed a free throw moments after hitting two to keep the Kansas lead at 5. Burke had scored on a layup to get Michigan back to within 3.

‘‘I’m so proud of my team because a lot of people say we’re young, but we stuck with it tonight,’’ Burke said. ‘‘I'm just so happy right now. We stayed together and we got the win.’’

The lead changed hands five times in overtime — the first OT game of the tournament — the last when Mitch McGary, who led Michigan with 25 points and 14 rebounds, hit a short jumper with Johnson in his face to put Michigan ahead for good, 83-82.

The Jayhawks got a stop and had about nine seconds to tie or win, but a jumbled possession ended with Naadir Tharpe missing a running jumper at the buzzer.

‘‘Well, this will go down as one of the toughest games obviously that we've been a part of . . . and I've been a part of,’’ Kansas coach Bill Self said.

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The Wolverines wiped out a 10-point Kansas lead on a 14-4 run in the final 2:52 of regulation. Burke had 8 points, including two 3-pointers, in the stretch.

Burke gave Michigan its first lead since early in the game with his long 3-pointer to make it 79-78 early in overtime. He hit a jumper on the next possession as well.

Burke was scoreless in the first half for the Wolverines, then got his team going by scoring 8 straight points early in the second half to momentarily cut the deficit to 2.

‘‘In the second half, coach told me to be more aggressive so I looked for my shot more,’’ he said.

But Kansas restored a 10-point lead built on dominating inside in the first half, this time with a 3-pointer and a tomahawk dunk on a breakaway by McLemore and a 3-point play from Johnson.

Johnson, who picked up three fouls in just three minutes of playing time in the first half, gave Kansas its biggest lead at 68-54 with a 3-pointer with just under 7 minutes left.

Travis Releford had 16 points for the Jayhawks, while Jeff Withey had 12 points and eight rebounds.

Kansas pushed out to a 10-point lead early by dominating around the basket. McLemore’s first basket was the first outside the paint as the Jayhawks scored 34 of their 40 first-half points from inside while shooting 69 percent.

Withey put Kansas ahead, 29-19, with a turnaround shot that had McGary shrugging at a teammate and saying, ‘‘I'm trying.’’

McGary wasn’t having nearly as much trouble on the offensive end, leading the Wolverines with 11 points and five rebounds in the first half. He picked up where he left off in the third round against Virginia Commonwealth, when he had season highs of 21 points and 14 rebounds.

Michigan pulled within 40-34 at the half when Nik Stauskas hit a 3-pointer and had chance for a four-point play when McLemore bumped him on the shot. But he missed the free throw.

The game was stopped less than two minutes in so officials could go to video review to call a flagrant foul against Johnson for a hit below the waist on McGary.